control.canonical_form

control.canonical_form(xsys, form='reachable')

Convert a system into canonical form.

Parameters

• xsys (StateSpace object) – System to be transformed, with state ‘x’

• form (str) –

  Canonical form for transformation. Chosen from:

  • ’reachable’ - reachable canonical form

  • ’observable’ - observable canonical form

  • ’modal’ - modal canonical form

Returns

• zsys (StateSpace object) – System in desired canonical form, with state ‘z’

• T ((M, M) real ndarray) – Coordinate transformation matrix, z = T * x

Examples

>>> Gs = ct.tf2ss([1], [1, 3, 2])
>>> Gc, T = ct.canonical_form(Gs)  # default reachable
>>> Gc.B
array([[1.],
       [0.]])

>>> Gc, T = ct.canonical_form(Gs, 'observable')
>>> Gc.C
array([[1., 0.]])

>>> Gc, T = ct.canonical_form(Gs, 'modal')
>>> Gc.A                                                    
array([[-2.,  0.],
       [ 0., -1.]])